January 17, 2017

Homework Help: statistics

Posted by sandy on Monday, March 18, 2013 at 12:32am.

Suppose we take a random sample of size n from a normal population with variance, σ2 . It can be shown that (n−1)s2/σ2 has a chi-square distribution with n−1 degrees of freedom, where s is the sample variance. Below is a random sample of size 8 drawn from a normal population. Use the above fact to compute a 95% confidence interval for the population variance, σ2 .
Sample 1: 11.6, 17.2, 15.0, 16.3, 22.9, 13.5, 16.4, 16.1

Below is a second random sample, independent from the first, of size 8 from a second normal population. Remembering that the F distribution is a ratio of independent chi- squares divided by their degrees of freedom, it can be shown that, under random, independent sampling, if the variances of the populations are equal, then s21/s2 has an F distribution with, in this case, 7 numerator and 7 denominator degrees of freedom (where the degrees of freedom are n − 1 for the corresponding samples). Test at α = .05 the null hypothesis that the variances are equal against the alternative that the variance of the first population is greater.
Sample 2: 17.7, 11.0, 17.0, 12.4, 10.8, 9.9, 17.2, 10.1

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